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EQUILIBRIUM OF RIGID BODIES
33
ment may be produced also by rotating the body to the position A" and then translating it to the position A'.
PROBLEMS.
1.   Show that in theorem II the order of the rotation and of the translation may be changed.
2.   Show that the converse of theorem II is true.
38. Theorem III.  The most general displacement of a rigid body can be obtained by a single translation and a single rotation.
Let A. and A' be any two positions occupied by the rigid body and P and P' be the corresponding positions of any one
of its particles. Then the body may be brought from A to Af by giving it a motion of translation which will bring the particle from P to P' and then rotating the body about a properly chosen axis through P'. A special case of this